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New Job requires MATH

A bit of background first-- I started a position palletizing in a fruit factory. Basically what we do is take dried fruit and package it.

As palletizer I am responsible for recording the total # of cases(total cases or TCS), the weight of the total cases (actual or A), the weight of the fruit that was used (total raw pounds or TRP), the weight of the fruit recovered from all nooks and crannies of the machinery at the end of the day (Salvage or S), and the percentage of fruit lost (%).

Now to find the loss percentage we subtract the S from the TRP to get TwoS (Total without Salvage), subtract A from TwoS to get the loss (L) in pounds, divide by TwoS, and multiply by 100 to get the final percentage.

So for me to learn this with a high school math level was well, fairly easy but it took a day or two.

But today I had a rough time, and this is where I need help.

To be brief, today we ran through 3.25 pallets of apricots (80 cases @ 28 lbs.), we packaged the fruit into 6 oz bags with 12 bags per case and 160 cases per pallet. 201 cases are shipped to vendor A, while the rest are shipped to vendor B. Due to the small weight of the bags, its difficult for the machine to produce accurate results, resulting in a loss due to overweight bags. Because of this, my lead gives me direction to manipulate the numbers so the loss percentages for both orders are in the same ballpark. Anything under 3% is considered acceptable (although sometimes there's nothing that can be done about a high percentage).

So what this means is that in reality 42 boxes were used to produce the 201 cases, but due to the fact its a small amount with overweight bags the % is around 14% (completely unacceptable). We have to bring that down to 3% by taking or removing TRP from A to B. We also have to pretend there was at least a little salvage in A's order which means pretending more TRP was used (The S from A will then be added into B's TRP).

What I'm now wondering is what kind of math can be used to calculate this so I can study on my own. While this may be simple to most mathematicians, it is highly stressful for me to calculate due to the fact it's one of many tasks I am required to complete. That said I'm looking for the fastest possible process to calculate this so that I dont have to think so much and I can let the process do the work.

Anyway I hope I explained this clearly. If any clarification is needed please ask and I will reply promptly. Thank you anyone who reads and shares their thoughts.

Surely, with 12*160 = 1920 bags per pallet, the weight of the bags can be accounted for...? I mean, use a postage scale to get the weight of one bag (or a dozen bags, or whatever), and multiply to get a known value that you can subtract from the total ("gross"?) weight, to get the net weight without the bags.

Surely, with 12*160 = 1920 bags per pallet, the weight of the bags can be accounted for...? I mean, use a postage scale to get the weight of one bag (or a dozen bags, or whatever), and multiply to get a known value that you can subtract from the total ("gross"?) weight, to get the net weight without the bags.

Our machine operator tries to do this, but the problem with this is the expectations from our superiors. If a 6 oz. bag has 7 oz. of fruit inside, its considered a loss of 1 oz. Due to the fast pace environment its impossible to take the time to remove the excess fruit, and with a small order like 200 cases a loss of say 15 lbs is a ridiculously high % while an order of 800 cases with a loss of 150 lbs is nowhere near as high (allowing wiggle room for numbers between orders.)

Which is where my job comes in. I basically need to lower the loss for the small order by any means necessary to keep it around 3% while at the same time maintaining a similar percentage for the order with more cases.

What I'm wondering is what area of math to study in to become proficient in dealing with percentages and averaging, if there are any ways to process information with a missing variable, and realistic estimating.

Our machine operator tries to do this, but the problem with this is the expectations from our superiors. If a 6 oz. bag has 7 oz. of fruit inside, its considered a loss of 1 oz. Due to the fast pace environment its impossible to take the time to remove the excess fruit, and with a small order like 200 cases a loss of say 15 lbs is a ridiculously high % while an order of 800 cases with a loss of 150 lbs is nowhere near as high (allowing wiggle room for numbers between orders.)

Which is where my job comes in. I basically need to lower the loss for the small order by any means necessary to keep it around 3% while at the same time maintaining a similar percentage for the order with more cases.

What I'm wondering is what area of math to study in to become proficient in dealing with percentages and averaging, if there are any ways to process information with a missing variable, and realistic estimating.

As I see it - you need to work with the dispenser.

If dispenser puts out 6 ± 1 oz (~17% error) then after all said and done that will be expected error! You need to sit down with your supervisor and discuss it. Without seeing your whole operation - it will be very difficult for us to suggest a method to lower your losses.

“... mathematics is only the art of saying the same thing in different words” - B. Russell

The thing about packaging mass quantities of fruit as fast as possible: it's messy, and handling it is unpredictable. One of my responsibilities is to collect salvage where it gathers; salvage is edible fruit that hasnt made itself into a bag.

In my example given I stated there was 650 lbs. of salvage. This is not a loss(L) as it is reusable, but is now recorded as a variable seperate from the total raw pounds (lbs.).

If dispenser puts out 6 ± 1 oz (~17% error) then after all said and done that will be expected error! You need to sit down with your supervisor and discuss it. Without seeing your whole operation - it will be very difficult for us to suggest a method to lower your losses.

In a perfect world...

this would be an option. It's not. The machine operator (dispenser) speaks maybe a lick of English. If I bring the 'expected losses' thing to my supervisor she'll say she knows but it's still unacceptable, and thus must be fixed

which is what brought me here in the first place. My math on knowledge relies solely on my memory of math class in high school, and I've somehow figured out this much, forgot it, then figured it out again. I'm still forgetting stuff (real silly stuff, too) so I'm trying to find out what the most relevant subject of math is so I can study it, thataway when the 15 minutes I have to run numbers at the end of the day comes I can do it without a sweat.